Motivated by a wide range of applications in various fields of physics and materials science, we consider a generalized approach to the evolution of a polydisperse ensemble of spherical particles in metastable media. An integrodifferential system of governing equations, consisting of a kinetic equation for the particle-size distribution function (Fokker–Planck type equation) and a balance equation for the temperature (concentration) of a metastable medium, is formulated. The kinetic equation takes into account fluctuations in the growth/reduction rates of individual particles, the velocity of particles in a spatial direction, the withdrawal of particles of a given size from the metastable medium, and their source/sink term. The heat (mass) balance equation takes into account the growth/reduction of particles in a metastable system as well as heat (mass) exchange with the environment. A generalized system of equations describes various physical and chemical processes of phase transformations, such as the growth and dissolution of crystals, the evaporation of droplets, the boiling of liquids and the combustion of a polydisperse fuel. The ways of analytical solution of the formulated integrodifferential system of equations based on the saddle-point technique and the separation of variables method are considered. The theory can be applied when describing the evolution of an ensemble of particles at the initial and intermediate stages of phase transformation when the distances between the particles are large enough, and interactions between them can be neglected.

Models for the prediction of the solid/liquid interfacial energy in pure substances and binary alloys, respectively, are reviewed and extended regarding the temperature and concentration dependence of the required thermodynamic entities. A CALPHAD-type thermodynamic database is used to introduce temperature and concentration dependent melting enthalpies and entropies for multicomponent alloys in the temperature range between liquidus and solidus. Several suitable models are extended and employed to calculate the temperature and concentration dependent interfacial energy for Al–FCC with their respective liquids and compared with experimental data.

A microstructural informed thermodynamic model is utilized to tailor the pseudoelastic performance of a series of Fe–Mn–Al–Ni shape‐memory alloys. Following this approach, the influence of the stability and the amount of the B2‐ordered precipitates on the stability of the austenitic state and the pseudoelastic response is revealed. This is assessed by a combination of complementary nanoindentation measurements and incremental‐strain tests under compressive loading. Based on these investigations, the applicability of the proposed models for the prediction of shape‐memory capabilities of Fe–Mn–Al–Ni alloys is confirmed. Eventually, these thermodynamic considerations enable the guided enhancement of functional properties in this alloy system through the direct design of alloy compositions. The procedure proposed renders a significant advancement in the field of shape‐memory alloys.

Critical evaluation of the phase equilibria, thermodynamics and crystal structures data in binary systems.System Li-Sn

The thermodynamic description of the fcc phase in the Al-Cu system has been revised, allowing for the prediction of metastable fcc/liquid phase equilibria to undercoolings of Δ T = 421 K below the eutectic temperature. Hypoeutectic Al-Cu alloys that are prone to pronounced microsegregation were solidified containerlessly in electromagnetic levitation. Solidus and liquidus concentrations were experimentally determined from highly undercooled samples employing energy-dispersive X-ray analysis. Solid concentrations at a rapidly propagating solid/liquid interface were additionally calculated using a sharp interface model that considers all undercoolings and is based on solvability theory. Modelling results (front velocity versus undercooling) were also corroborated by in situ observation with a high-speed camera. A newly established thermodynamic description of the fcc phase in Al-Cu is compatible with existing CALPHAD-type databases. Inconsistencies of previous descriptions such as a miscibility gap between Al-fcc and Cu-fcc on the Al-rich side, an unrealistic curvature of the solidus line in the same composition range or an azeotropic point near the melting point of Cu, are amended in the new description. The procedure to establish the description of phase equilibria at high undercoolings can be transferred to other alloy systems and is of a general nature. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.